Set edge as axis for surface rotation
To rotate the faces around a specific edge, change to Edge Selection Mode, select all the edges of the face you want to rotate and select the edge that the face will be rotating around as last. 

Set Pivot Point as Active Element and change Transform Orientation to Normal. 

To rotate the face around that edge hit R button, then Y button twice, then type rotational angle and hit Enter.

For dodecahedron faces to meet the rotational angle should be around 63.5 degrees (arccos(1/√5)) from the grid floor. 

To use the function for precise rotation, after hitting R button type:

*180*acos(1/sqrt(5))/pi


To change the angle to negative or positive use Ctrl+- buttons